Find the mean proportion between :
25, 15

Answer

To find the mean proportion between 25 and 15, we can follow these steps:

### Step 1: Define the Mean Proportion
Let the mean proportion be \( x \). According to the definition of mean proportion, we can express it as:
\[ \frac{25}{x} = \frac{x}{15} \]

### Step 2: Cross Multiply
Cross multiplying gives us:
\[ 25 \cdot 15 = x \cdot x \]
This simplifies to:
\[ 25 \cdot 15 = x^2 \]

### Step 3: Calculate the Product
Now, calculate \( 25 \cdot 15 \):
\[ 25 \cdot 15 = 375 \]
So, we have:
\[ x^2 = 375 \]

### Step 4: Solve for \( x \)
To find \( x \), we take the square root of both sides:
\[ x = \sqrt{375} \]

### Step 5: Simplify the Square Root
We can simplify \( \sqrt{375} \):
\[ \sqrt{375} = \sqrt{25 \cdot 15} = \sqrt{25} \cdot \sqrt{15} = 5\sqrt{15} \]

### Final Answer
Thus, the mean proportion between 25 and 15 is:
\[ x = 5\sqrt{15} \]

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